Simplifying Radicals

Simplifying Radicals

1. Examples of Radical Expressions: square roots, cube roots, fourth roots and so on

2. Examples Problem: √36

   • - Ask yourself what number times itself is going to give you in this case 36
     • When you ask yourself that hopefully, you answered 6 because 6*6=36.
       • So our answer would be + or - 6
       • So is 6 our answer? Well not quite because when dealing with square roots, it's not just a positive times a positive number, but it could also be negative. In this case, you could not only do 6*6=36 but you could also square a negative 6 and get a positive 36.
         • The symbol just lets us know that in this case the square root of 36 could be positive or negative.

3. Radical Expressions that are not perfect squares:

   • Example: √50 The 50 will factor down to √2 * √25
     • 1. To find the simplified version of this radical we much first work with some factors in this case of 50 & breaks it down. 2. List factors fo the number 3. Look for the ones that are perfect squares when looking for factors. 4. When finding the factors they also need to be under a radical sign because the 50 is under one.
     • The √25 simplifies down to 5*5
       • Our answer would then be + or - 5√2
         • When we rewrite a radical that has been simplified we always want to put the integer number in front.

4. Radical Problems (More Complex)

   • Sometimes your variables will contain exponents underneath the radial sign.s.
     • 1. Break the number into factors, in this case, we are dealing with 20. 2. Try to find the factors that are perfectly similar. 3. Ignore the variables for now
       • Example: √20x²y^(4). He can be simplified down to √4 *√5. Then later 4 can be simplified down to 2*2
         • The numbers we are focusing on are 5, 2 and 2
           • So this is equal to + or - 2√5
             • Since, we ignored the variables at the beginning now it is time to finsh up this problem.
               • You could do this by doing √x²y^(4) which will then be changed into this (x²y^(4) 1/2.
                 • Once solved our answer overall is + or - 2xy²√5